Generally, a connector includes a female connector and a male connector. For example, one of the conventional connectors has a tubular outer housing as a female connector and an inner housing which is received in the outer housing, and a plurality of female terminals are provided in the end surface of the inner housing. Further, the connector has a bottomed tubular counterpart housing as the male connector, and the plurality of male terminals are provided in the inner bottom surface of the counterpart housing. Further, when the male connector is fitted to the female connector, the end surface of the inner housing and the inner bottom surface of the counterpart housing are brought into close contact with each other, and the female terminal and the male terminal are connected electrically (for example, see JP-A-H09-180818).